1. The problem statement, all variables and given/known data Let V=Mn(F) be the space of all nxn matrices over F; define TA=(1/2)(A+transpose(A)) for A in V. Verify that T is not only a linear operator on V, but is also a projection. 2. Relevant equations A is a projection when A squared=A. 3. The attempt at a solution I don't see how this works since clearly (1/2)(A+transpose(A)) squared does not equal (1/2)(A+transpose(A)) for all matrices. What am I doing wrong?